\textbf{114.} Suppose $f(x) = \begin{cases} -1 & x < -1 \\ x & -1 \leq x \leq 1 \\ 1 & x > 1 \end{cases}$ and $g(x) = 1 - x^2$. The number of elements of the set of points where $g \circ f$ and $f \circ g$ are \textbf{not} differentiable is:
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(1) $2$ \hfill (2) $3$ \hfill (3) $4$ \hfill (4) $5$
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